Mathematics 56 (number)

regular 56-gon, associated pythagoreans typhon

56 is:

the sum of first 6 triangular numbers (making tetrahedral number).
the number of ways choose 3 out of 8 objects or 5 out of 8 objects, if order not matter.
the sum of 6 consecutive primes (3 + 5 + 7 + 11 + 13 + 17).
a tetranacci number , pronic number.
the sum of sums of divisors of first 8 positive integers.
a semiperfect number, since 56 twice perfect number.
a partition number - number of distinct ways 11 can represented sum of natural numbers.
an erdős–woods number, since possible find sequences of 56 consecutive integers such each inner member shares factor either first or last member.
the known number n such φ(n − 1)σ(n − 1) = φ(n)σ(n) = φ(n + 1)σ(n + 1), φ(m) euler s totient function , σ(n) sum of divisor function, see  a244439.

the maximum determinant in 8 8 matrix of zeroes , ones 56.

plutarch states pythagoreans associated polygon of 56 sides typhon , associated polygons of smaller numbers of sides other figures in greek mythology. while impossible construct perfect regular 56-sided polygon using compass , straightedge, close approximation has been discovered claimed might have been used @ stonehenge, , constructible if use of angle trisector allowed since 56 = 2 × 7.